[1]} considered the time-evolution through a quantum critical point, at which the gap between the ground state and the first
excited state vanishes and adiabaticity breaks down.
The 1-d transverse-field Ising model
is mapped by the Jordan-Wigner transformation to a set of independent Landau-Zener Hamiltonians, for which \(H_1\)  is known [2]}. However \(H_1\) 
in real space is highly nonlocal. They also proposed approximate
STA by truncating the CD terms so that they have
finite ranges. An alternative scheme to avoid nonlocal CD term by tailoring the form of the CD interactions
is also proposed [3]}. [4]} proposed protocols which minimizes excitation production in a closed quantum critical system
driven out of equilibrium.
